3 papers
math.CA2024
Kapaev's global asymptotics of the fourth Painlevé transcendents. Elliptic asymptotics
Shun Shimomura
For the fourth Painlevé transcendents we derive elliptic asymptotic representations, which were announced by late Professor Kapaev without proofs. Then we newly obtain related resu…
math.CA2018
Three-Parameter Solutions of the PV Schlesinger-Type Equation near the Point at Infinity and the Monodromy Data
Shun Shimomura
For the Schlesinger-type equation related to the fifth Painlevé equation (V) via isomonodromy deformation, we present a three-parameter family of matrix solutions along the imagina…
math.CA2016
Critical behaviours of the fifth Painlevé transcendents and the monodromy data
Shun Shimomura
For the fifth Painlevé equation, we present families of convergent series solutions near the origin and the corresponding monodromy data for the associated isomonodromy linear syst…